Error using angle measure feature of measure it
I notice from your screengrab that none of the selected vertices is active. That suggests maybe you used something like Box or Circle-select to select them. 

Because, (even if you didn't) you might have selected more than one vertex simultaneously, they don't have a selection order. The MeasureIt Angle display needs to know in which order the vertices were selected.. 

Does it work if you use the default 'Tweak' selection mode, and select the vertices one at a time?